Were hadiths so widespread that hadith imams memorized hundreds of thousands, or so few that it was difficult to find an "aziz" hadith?

The enormous numbers of hadiths refer to the number of texts (matn) with their chains of narration (isnad). A single text can have dozens of chains of narration, and each chain is counted as a hadith. These texts may also include sayings of the Companions and the Successors.

The Aziz hadith is what is narrated by at least two from two. It is called so either due to its strength by coming through another path, or due to its rarity.

The condition of having two narrators in one of the layers of the chain makes it rare, as most hadiths have multiple chains, but their pivot might be a single narrator in some layers, and then their paths multiply in later layers, such as the hadith "Indeed, actions are by intentions."